Head Loss As an Explanation of the Steal Phenomenon in Microvascular Surgery

Abstract

Vascular steal has been cited to help explain end-organ ischemia after microvascular reconstruction. Attempts to clarify a mechanism of vascular steal have been made by modeling blood circulation after a simple electrical circuit, suggesting that the free flap provides a path of least resistance for blood flow and thereby compromises end-organ perfusion. We present a case of a posterior medial thigh perforator flap for the reconstruction of a diabetic foot ulcer in a patient with a single vessel providing inflow to the foot. In the context of this case, we provide a novel explanation for the steal phenomenon using the Hagen-Poiseuille law and the property of head loss in fluid dynamics and discuss how the vessel size of the free flap may contribute to a steal phenomenon.

Keywords: head loss; lower extremity; perforator flap; posterior medial thigh flap; steal phenomenon.

Figure 1

Defect, flap harvest, and flap inset. (a) Lower extremity defect: preoperative vascular workup revealed an occlusion of the anterior tibial artery at its origin, a toe-brachial index of 0.10, and flow to the foot only from the posterior tibial artery. (b) Medial thigh posterior free flap based on a single perforator identified with a Doppler probe and found to traverse the semimembranosus muscle and to originate from the profundus femoral artery. Pedicle length was 6 cm with an artery of 1.0 mm in diameter. (c) Closure, end-to-side anastomosis done to the posterior tibial artery.

Figure 2

Schematic of vessel anastomosis and flow calculations. (a) A cartoon schematic of the flap and corresponding anastomosis with the main end-organ artery. (b) Schematic of a section of the blood vessel with an arrow showing direction of the flow of blood. R₁ and Q₁ on either side designate the resistance and flow rate, respectively. Below is a schematic of the conduit's analogous electrical circuit with resistor R₁ shown for clarity. (c) The same section of blood vessel as in (b) is shown with new anastomosis sutured in an end-to-side “T-branch” fashion. Arrows show direction of blood flow. Q₂ represents the flow rate proximal to the junction, which also represents the new overall flow rate. Q₃ = Q₁ represents the flow rate distal to the junction being equal to the flow rate in (b). The electrical circuit shown below is used to help illustrate the addition of the vasculature in parallel, represented by resistors R₁ and R₂. R₂ and Q₄ designate the resistance and flow rate of the perforator for the free flap, respectively. (d) The Hagen-Poiseuille law of fluid dynamics, where Q is the flow rate, R is the total resistance, and P is the total pressure at any given location. (e) Resistance experienced by blood traveling in a vessel, where η is the blood viscosity (0.0035 Pa·s), l is the vessel length, and r is the radius of the vessel. (f) Total resistance for n resistors in parallel. (g) Expression for flow rate using the Hagen-Poiseuille law for a single vessel. (h) Expression for flow rate using the Hagen-Posiseuille law when vessels are added in parallel. A and B designate the radius and length of the main branch and the perforating vessel from the donor flap, respectively.

Figure 3

Flow rate schematic. (a) Schematic of blood vessel, where r₁ represents the radius of the vessel perforating the flap, Q₂ represents flow rate proximal to junction, which is the same flow rate in Figure 2c, h_L1 represents the head loss at the junction, and Q₅ < Q₂ represents the flow rate distal to the junction being less than the flow rate proximal to the junction. (b) Schematic of the blood vessel, where 2r₁ represents a doubling of the perforating flap vessel as compared with (a), h_L2 > h_L1 represents greater head loss compared with (a) when the radius of the perforating flap vessel is doubled, and Q₇ < Q₅ denotes the flow rate distal to the junction being less than the flow rate distal to the junction in (a).